Homotopy equivalence

We exhibit a counterexample to Elliott’s classification conjecture for simple, separable, and nuclear C∗ -algebras whose construction is elementary, and demonstrate the necessity of extremely fine invariants in distinguishing both approximate unitary equivalence classes of automorphisms of such algebras and isomorphism classes of the algebras themselves.

17p dontetvui 17-01-2013 67 5   Download

We define and study sl2 -categorifications on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the simple reflection. We construct categorifications for blocks of symmetric groups and deduce that two blocks are splendidly Rickard equivalent whenever they have isomorphic defect groups and we show that this implies Brou´’s abelian defect group conjecture for symmetric groups. e We give similar results for general linear groups over finite fields. ...

55p dontetvui 17-01-2013 50 8   Download

The purpose of this paper is to prove that the stable homotopy category of algebraic topology is ‘rigid’ in the sense that it admits essentially only one model: Rigidity Theorem. Let C be a stable model category. If the homotopy category of C and the homotopy category of spectra are equivalent as triangulated categories, then there exists a Quillen equivalence between C and the model category of spectra. Our reference model is the category of spectra in the sense of Bousfield and Friedlander [BF, §2] with the stable model structure. The point of the rigidity theorem is that its...

28p noel_noel 17-01-2013 49 6   Download

We prove that the classical Oka property of a complex manifold Y, concerning the existence and homotopy classification of holomorphic mappings from Stein manifolds to Y, is equivalent to a Runge approximation property for holomorphic maps from compact convex sets in Euclidean spaces to Y . Introduction Motivated by the seminal works of Oka [40] and Grauert ([24], [25], [26]) we say that a complex manifold Y enjoys the Oka property if for every Stein manifold X, every compact O(X)-convex subset K of X and every continuous map f0 : X → Y which is holomorphic in an...

20p noel_noel 17-01-2013 50 5   Download

There are very few examples of Riemannian manifolds with positive sectional curvature known. In fact in dimensions above 24 all known examples are diffeomorphic to locally rank one symmetric spaces. We give a partial explanation of this phenomenon by showing that a positively curved, simply connected, compact manifold (M, g) is up to homotopy given by a rank one symmetric space, provided that its isometry group Iso(M, g) is large. More precisely we prove first that if dim(Iso(M, g)) ≥ 2 dim(M ) − 6, then M is tangentially homotopically equivalent to a rank one symmetric space or M...

63p noel_noel 17-01-2013 53 5   Download

For each k ∈ Z, we construct a uniformly contractible metric on Euclidean space which is not mod k hypereuclidean. We also construct a pair of uniformly contractible Riemannian metrics on Rn , n ≥ 11, so that the resulting manifolds Z and Z are bounded homotopy equivalent by a homotopy equivalence which is not boundedly close to a homeomorphism. We show that for these lf spaces the C ∗ -algebra assembly map K∗ (Z) → K∗ (C ∗ (Z)) from locally finite K-homology to the K-theory of the bounded propagation algebra is not a monomorphism ...

21p tuanloccuoi 04-01-2013 37 6   Download

Allen Hatcher Copyright c 2000 by Allen Hatcher Paper or electronic copies for noncommercial use may be made freely without explicit permission from the author. All other rights reserved. .Table of Contents Chapter 0. Some Underlying Geometric Notions Homotopy and Homotopy Type 1. Cell Complexes 5. . . . . . 1 Operations on Spaces 8. Two Criteria for Homotopy Equivalence 11. The Homotopy Extension Property 14. Chapter 1. The Fundamental Group 1. Basic Constructions . . . . . . . . . . . . . 21 25 . . . . . . . . . . . . . . . . . . . . . ....

0p tiramisu0908 31-10-2012 47 2   Download

This book grew out of courses which I taught at Cornell University and the University of Warwick during 1969 and 1970. I wrote it because of a strong belief that there should be readily available a semi-historical and geometrically motivated exposition of J. H. C. Whitehead's beautiful theory of simple-homotopy types; that the best way to understand this theory is to know how and why it was built.

126p taurus23 27-09-2012 43 2   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Abstract We exhibit an explicit homotopy equivalence

14p lame_266 12-09-2011 44 2   Download